A free-form surface is used for the bodies of various industrial products, such as ships, automobiles and airplanes, having both functionality and beauty, and is used for designing beautiful artistic shapes, such as home electric products and the appearance of many consumer goods. These curved surfaces are called a “Class A surface”. In order to estimate the beauty of a Class A surface, various evaluation methods have been proposed and used.
As the use of three-dimensional CAD and CAM systems spread, the curved surface quality evaluations of curved surface of design shapes are more extensively used in industrial design and manufacturing fields. In the case of the design of the outside plate body of an automobile, for example, a designer irradiates parallel lights from a fluorescent lamp on a clay model, visually observes the reflected light projected on the surface of the clay model, observes the appearance of the shape of the reflection light which the reflection light forms on the formed surface, and detects the repair sections by the distortion of reflection lines.
Shape evaluation by simulation on a computer has been proposed instead of quality evaluation by irradiating parallel lights from a fluorescent lamp on an actual model has been proposed. As a method for forming light lines on an evaluation target surface on a computer, evaluation methods using Isophotes, Reflection lines or Highlight lines are known. These evaluation methods are inspection method using a single differentiation of the evaluation surface. These reflection lines and highlight lines for shape evaluation are collectively called “characteristic lines”.
For shape evaluation by Isophotes, a curve with a predetermined illuminance on the curved surface created by a point light source at an infinite point in a direction specified by the user is used. These curves are used for detecting the distortion of the curved surface. If the curved surface has CM continuity, then Isophotes lines are CM−1 continuous (Non-patent Documents 1 and 2).
Shape evaluation by reflection lines is based on simulation of a mirror image of lights irradiated from a light source of a parallel line group viewed from a fixed point on a smooth curved surface, and a deviation from the smooth shape of the curved surface is detected by the distortion of the reflection lines. The deviation of the curved surface can be corrected by correcting the distortion of the reflection lines.
Generating reflection lines on a trimmed NURBS surface using the mapping function of Blinn-Newell type reflection, which is simple and can be physically acquired, has also been proposed (Non-patent Document 3). Also in Non-patent Document 4, calculating the reflection lines of a small chained annular light source group along a straight line has been proposed.
FIG. 27A is a diagram depicting a shape evaluation by a reflection line. In FIG. 27A, parallel linear lights are irradiated from a line light source 101 on an evaluation surface 100, and lights reflected on the evaluation surface 100 are observed at a view point E. The view point E and the line light source 101 are at symmetric angle positions (angle θ) with respect to a normal line N on the evaluation surface 100, and the line light source 101 is observed at view point E as a reflection line 102. In the case of the shape evaluation based on a reflection line, the reflection line 102, projected on the evaluation surface 100 with respect to the line light source 101 and the view point E, is determined by performing computer simulation.
Shape evaluation using an oval curve instead of a linear reflection line has also been proposed (Non-patent Document 5). FIG. 28 are diagrams depicting the shape evaluation based on the oval curve. According to this non-patent document, when a point Ps is set in a space in FIG. 28A, a point, where an angle formed by the vector r* and vector from the point S to the point Ps becomes α, is determined out of the points S on the evaluation surface on which the incident light V* reflects in the r* direction when the points Ps are set in space. The set of the points S on the evaluation surface at which the angle α formed by these two vectors is similar to an isocline with angle α, which is determined as a reflection line (FIG. 28B). Here the symbol “*” indicates a vector.
Shape evaluation based on a highlight line, on the other hand, is a shape evaluation based on a reflection line which is simplified. Since the highlight line does not depend on a view point, the calculation of a view point is unnecessary, unlike the case of shape evaluation based on a reflection line (Non-patent Document 6).
FIG. 29A and FIG. 29B are diagrams depicting shape evaluation based on highlight lines. In FIG. 29B, a curve on the evaluation surface 100, of which distance between the extension of the normal line N on the evaluation surface 100 and the line light source 101 is within a predetermined range, is observed as a highlight line 103.
Since the simulation of the highlight line does not require a view point, the computing time is decreased.
In shape evaluation based on a highlight line, a method for automatically updating control points on an NURBS surface and for determining a required shape by specifying a shape of highlight lines projected on the NURBS surface has been proposed (Non-patent Document 7), and a method for directly controlling highlight lines using an NURBS boundary Gregory patch has been proposed (Non-patent document 8).
Also a method for removing local irregularities of the NURBS surface by modifying the highlight lines in real-time interactive design has been proposed (Non-patent Document 9).
Also a method for generating dynamic highlight lines on a locally deformed NURBS surface using a Talor development method instead of a follow up method, of which processing time is long, has been proposed (Non-patent Document 10).    Non-patent Document 1. N. M. Patrikalakis and T. Maekawa: Shape Interrogation for Computer Aided Design and Manufacturing, Heidelberg, Germany: Springer-Verlag, 2002    Non-patent Document 2. T. Poeschl: Detecting surface irregularities using isophotoes, Computer Aided Geometric Design, 1(2), 163-168, 1984    Non-patent Document 3. I. Choi and K. Lee: Efficient generation of reflection lines to evaluate car body surfaces, Mathematical Engineering in Industry, 7(2), 233-250, 1998    Non-patent Document 4. T. Kanai: Surface interrogation by reflection lines of a moving body, Bachelor's Thesis, The University of Tokyo, Department of Precision Machinery Engineering, Tokyo, Japan, 1992, in Japanese at—http://web.sfc.keio.ac.jp/kanai/rline/bth.pdf    Non-patent Document 5. Gershon Elber: Curve Evaluation and Interrogation on Surfaces, Graphical Models, Vol. 63, 197-210, 2001    Non-patent Document 6. K. P. Beier and Y. Chen: Highlight-line algorithm for real time surface quality assessment, Computer-Aided Design, 26(4), 268-277, 1994    Non-patent Document 7. Y. Chen, K. P. Beier and D. Papageorgiou: Direct highlight-line modification on NURBS surfaces, Computer-Aided Geometric Design, 14(6), 583-601, 1997    Non-patent Document 8. J. Sone and H. Chiyokura: Surface highlight control using quadratic blending NURBS boundary Gregory patch, Journal of Information Processing Society of Japan, 37(12), 2212-2222, 1996, in Japanese    Non-patent Document 9. C. Zhang and F. Cheng: Removing local irregularities of NURBS surfaces by modifying highlight lines, Computer-Aided Design, 30(12), 923-930, 1998    Non-patent Document 10. J. H. Yong, F. Cheng, Y. Chen, P. Stewart and K. T. Miura: Dynamic highlight line generation for locally deforming NURBS surfaces: Computer-Aided Design, 35(10), 881-892, 2003    Non-patent Document 11. J. E. Hacke: A simple solution of the general quartic: American Mathematical Monthly, 48(5), 327-328, 1941